Annika Sorenstam, the 1998 and 2002 champion, posted a 4-under-par 67 to take second place. Mi Hyun Kim is alone in third at minus-2, while Jeong Jang is the final player in red figures at 1-under-par 70 on the Bay Course at Seaview Marriott Resort & Spa.
There were no delays Friday despite the fact that rain fell steadily throughout the round.
Inkster, who won this title in 1986 and 1988, rolled in a 25-foot birdie putt on the third to get her round going. She then stuck a sand-wedge 10 feet from the cup at No. 8 to set up her second birdie.
The 44-year-old came right back with a 3-foot birdie putt on the ninth. Inkster made three straight as she drained a 25-foot birdie try on the 10th. Her run ended with a bogey on the par-3 11th after she missed the green left.
Inkster got that stroke back with a birdie on the 15th. She pitched in for eagle on the 16th to move to 6 under. The five-time Solheim Cup performer bogeyed the 17th, but came back by sinking a 4-foot birdie putt at the last for a two-shot lead.
'It was extremely difficult. The wind was blowing. The rain just did not let up all day long until maybe we got to the 18th green,' Inkster said. 'It was just a driving rain all day. I made a couple long putts and I chipped in twice, but I missed a couple short ones, too.'
Sorenstam got off to a tough start as she bogeyed the par-4 second. The Swede, though, pitched her third shot to the par-5 third to four feet and rolled in that putt for birdie.
The Kraft Nabisco champion tripped to another bogey at the sixth, but around the turn, Sorenstam drained a 35-foot birdie putt on the 10th to get back to even par.
Sorenstam, who is the two-time defending champion at next week's McDonald's LPGA Championship, dropped a sand-wedge within 10 feet of the cup to set up a birdie on the 13th.
The 60-time winner on the LPGA Tour ran in a 6-foot birdie putt on 15 to get to minus-2. Sorenstam's second to the par-5 16th came to rest 5 feet from the cup. She converted the eagle putt to take second place.
'I really didn't get off to a good start, but then again it wasn't the nicest day of golf today,' said Sorenstam. 'I thought it was quite difficult, especially the second hole which I bogeyed. It was tough on the front, it really was. Then, I made a long putt on 10 and that kind of kick started my back side and I played really good.'
Se Ri Pak, the 1999 champion here, posted an even-par round of 71. She was joined there by Nancy Harvey, Pat Hurst, last week's winner Jimin Kang, Heather Bowie, Silvia Cavalleri, Laura Davies, Natalie Gulbis, Beth Bader, Shi Hyun Ahn, Carin Koch, Marilyn Lovander, Catriona Matthew and Kris Tschetter.
Defending champion Cristie Kerr shot a 3-over-par 74 and is in a tie for 50th place.